Question

$1litre$ of an ideal gas $(\gamma =1.5)$ at $300K$ is suddenly compressed to half its original volume.
Find the ratio of the final pressure to the initial pressure.

• A. 1.828
• B. 3.828
• C. 2.828
• D. 5.828

Answer 1

Answer: (C)

2.828

Given : 1 litre1 litre of an ideal gas (γ=1.5)(γ=1.5) at 300 K300 K is suddenly compressed to half its original volume.

Find the ratio of the final pressure to the initial pressure.

Solution:

$\gamma =1.5$ , T=300K , V=1L , V=1/2 L

The process is adiabatic as it is sudden

$P_1{V}_1^{\gamma }$=$P_2{V}_2^{\gamma }$ $\Rightarrow$ $P(1{)}^{1.5}=P_2(2{)}^{1.5}$

$\frac{P_2}{P_1}=2\sqrt{2}$ = 2.828

The Correct Opt = C